More than a third of voters remain undecided about whom to support in Boston’s mayoral race and no more than 12 percent of voters have coalesced around any one candidate, according to a new private poll, suggesting that any of several candidates could gain significant ground in the final month before the Sept. 24 preliminary election.

The survey, conducted by the Boston political consulting firm Sage Systems, found Councilor John R. Connolly and state Representative Martin J. Walsh in the lead, virtually tied at 12 percent and 11 percent, respectively. Suffolk County District Attorney Daniel F. Conley slotted third, at 9 percent.

Councilor Rob Consalvo and former state representative and city housing chief Charlotte Golar Richie were knotted at 7 percent, followed by two more councilors, Michael Ross and Felix G. Arroyo, at 6 percent.

Trailing, at 3 percent, were nonprofit executive John Barros and former health care executive Bill Walczak.

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Michael McLaughlin, Sage Systems vice president, said in an e-mail that the race is still fluid, noting that only 9 percentage points separate the top candidate from the bottom candidate. “The race is still up for grabs, and any candidate with a good financial base to meet, persuade, and motivate voters can win,” McLaughlin said.

Sage has business with two of the candidates, Ross and Consalvo, and its government relations president, former councilor Paul Scapicchio, is supporting Connolly. But Sage conducted the poll outside of those contracts and did not inform any of the candidates of the poll in advance, founder Frank Perullo told the Globe.

Conducted Aug. 21 and Aug. 22, the poll asked 821 voters who have voted in at least one municipal election since 2007 their opinions of the race. Its margin of error is plus or minus 2.7 percentage points.

The poll also appeared to show that racial identity has played a factor in voters’ decisions. Asked whether the candidate they intended to vote for was the same race as they are, 58 percent of voters who had picked a favorite said yes, while 31 percent said no.

Decided voters broke down less starkly along geographic lines. Thirty percent of them said their choice hailed from their home neighborhood, while 55 percent said they came from elsewhere.

Age appeared to matter even less in helping voters decide. Just 20 percent said that the candidate they planned to support was roughly their age, while 64 percent said they were not.

Of the voters who have settled on a candidate, nearly two-thirds said they would “definitely” back that person, while 34 percent said they were “somewhat sure” of their final choice.

Fifty-four percent of decided voters said they had met their candidate, while 42 percent said they had not. A Globe poll earlier this year found that 49 percent of residents had met Mayor Thomas M. Menino.

Voters appear uncertain about the résumé qualifications necessary to succeed him. Respondents were given a range of choices, corresponding to the candidates’ professional backgrounds, and asked which job best prepared the next mayor.

Sage System founder Frank Perullo said the polling numbers indicate the race has not captivated the city’s occasional voters.

Forty-seven percent said they were unsure. Nineteen percent chose councilor — a boost to Arroyo, former councilor Conley, Connolly, and Ross. Eight percent said state representative, a boon for Richie and Walsh. A background as district attorney or business leader earned 7 percent, while 4 percent each said nonprofit executive, labor union leader, or small business owner best trained a future mayor.

The 821 voters surveyed in the poll are considered more likely to vote than the average city voter because of their relatively recent history of going to the polls. Of those, 90 percent said they were “very” or “somewhat” likely to vote this year.

Perullo said that figure and the high percentage of undecided voters signal that the campaign has not captivated the attention of occasional voters. A vast field in the city’s first wide-open mayoral election since 1993 has failed, so far, to excite historic voter participation.

In the 2009 preliminary election, with Menino facing three challengers, fewer than 82,000 voters cast ballots. Perullo said this year’s turnout would probably be higher, but still at 100,000 votes or fewer.

Three candidates — Councilor Charles Yancey, radio station cofounder Charles Clemons, and former teacher David James Wyatt — were not included in the poll because their campaigns did not meet the thresholds set by the firm, Perullo said.